I have somewhat of a feeling that the Italianate pronunciation of Latin, used by the Church, is not held in as much intellectual esteem as the Classical pronunciation (which, I imagine, must have been dug out by means of phonetic and linguistic research, almost as if digging out archaeologically)... I must confess that for those of us who have familiarity with modern Romance Languages, the Vatican pronunciation is indeed a bit friendlier, due to its huge number of cognate sounding words... The Classical gets even more difficult to understand by mere earshot when you include the whole long/short vowel business... The first time I heard something read aloud strictly in Classical... with its maater paater fraaaaaaaaater, it sounded to me like Swedish...

Would any of you know if those scholars researching and writing about Medieval Latin would be more inclined to use Italianate phonetics... Has this indeed come to be perceived as rather obsolete (ironically, given the time-frame), or I am simply making the wrong inferences? Is this pronunciation used anywhere academically, other than obviously by the Church in its Seminaries?

You can bet that it is most widely used in Italy no matter which period the Latin text is from. And as far as I know classical pronuciation is not applied to nonclassical texts but that does not mean that the Italiante pronunciation is used instead. It is more likely that the pronunciation of such texts depends heavily on the country the scholar comes from. (Some people even make differences in their pronunciation depending on the country where the (medieval) text was written but I guess these are rare exceptions.)